Triangular Carrier Waveform Research Articles

Analysis and simulation of a single-phase seven-level inverter controlled by modified sinusoidal PWM technique

In this paper, a modified sinusoidal pulse width modulation (MSPWM) technique and a modified single-phase H-bridge seven-level inverter is proposed. The switching pulses for the proposed seven-level inverter are generated using a single triangular carrier waveform, a fully rectified sinusoidal signal, and three stepped reference signals (Uref1, Uref2 and Uref3). Using optimization technique, the magnitude of the stepped reference signal is determined so that the total harmonic distortion (THD) of the output voltage waveform is minimum and the fundamental component, RMS value of the voltage is improved for a given modulation index Ma as compared to the sinusoidal pulse width modulation (SPWM). By the implementation of the new scheme, the seven-level of the inverter output voltage level (+Vdc, +2Vdc/3, +Vdc/3, 0, −Vdc, −2Vdc/3, −Vdc) is obtained for any given modulation index. Similarly, if only two stepped reference signals are used then the inverter will act as a five-level inverter for any modulating index Ma. The proposed MSPWM and seven-level inverter are simulated on MATLAB/SIMULINK for R, R-L load and on a single-phase capacitor-start and capacitor-start-run Induction Motor.

Detailed and comprehensive mathematical modeling of flying-capacitor stacked multicell multilevel converters

Purpose – This study aims to propose a mathematical model for stacked multicell converters (SMCs), to be exploited in the analytic determination of natural voltage balancing dynamics of the flying-capacitor (FC) stacked multicell multilevel converters, i.e. investigations of the start-up behavior, dynamic response, and natural voltage balancing phenomenon. Design/methodology/approach – The crux of the proposed strategy is based on the closed-form analytic solution derivation for the switching functions used in the switching of the SMCs operated under phase disposition (PD) and phase shifted carrier (PSC) pulse width modulation (PD-PSC-PWM) technique. Hence, the suggested approach develops an analytic solution for the Fourier series and associated Fourier coefficients pertinent to the switching functions of the SMCs by obtaining the switching instants of the PD-PSC-PWM modulator in terms of Kapteyn series when the frequency of the triangular carrier waveform (fc) and that of the sinusoidal reference waveform (fr) have an integer ratio, i.e. f c · f r −1=k, k∈N. Findings – This approach results into a model, first order differential equation based model, which can be readily developed for the SMCs with any number of levels expediting the investigation of their performance. Furthermore, by an experimental scrutiny conducted on a 4×2-cell-nine-level topology of an SMC, it is inferred that under PD-PSC-PWM modulation technique, FC voltages balance naturally for higher number of stacks and cells, therefore the natural balancing exist for high-level SMCs. Research limitations/implications – Despite the sophistication of the proposed methodology and mathematical model, this study presents an alternative approach with high potential of applicability for derivation of the multilevel converter mathematical model exploiting the Kapteyn (Bessel-Fourier) series. Practical implications – Numeric computation results of the proposed analytic model for the SMCs and the simulation results as well as investigational measurements taken from 2×2-cell-five-level and 4×2-cell-nine-level experimental set-ups are presented in order to substantiate the suggested approach, derived model, and verification of natural balancing. Originality/value – This article and its innovations are original.

Analytical modelling of single‐phase stacked multicell multilevel converters exploiting Kapteyn (Fourier–Bessel) series

This study proposes a mathematical model for stacked multicell (SM) converters (SMCs), to be exploited in the analytic determination of the natural voltage balancing dynamics of the SMCs, that is, investigation of the start-up behaviour, dynamic response and natural voltage balancing phenomenon. The crux of the proposed strategy is based on the closed-form analytic solution derivation for the switching functions used in the switching of the SMCs operated under phase disposition (PD) and phase-shifted carrier (PSC) pulse-width modulation (PD–PSC-PWM) technique. Hence, the suggested approach develops an analytic solution for the Fourier series and associated Fourier coefficients pertinent to the switching functions of the SMCs by obtaining the switching instants of the PD–PSC-PWM modulator in terms of ‘Kapteyn series’ when the frequency of the triangular carrier waveform (f c) and that of the sinusoidal reference waveform (f r) have an integer ratio, that is, f c f r −1 = k, k ∈ ℕ. This strategy results into a model (‘first-order differential equation based model’) which can be readily developed for the SMCs with any number of levels expediting the investigation of their performance. Numeric computation results of the proposed analytic model for the SMCs and simulation results as well as measurements taken from an experimental set-up are presented in order to validate the suggested approach and derived model.

A Carrier - Based Pulse Width Modulation Control Strategies for Cascaded Multilevel Inverter

In this paper, three novel multicarrier pulse width modulation techniques which uses stepped carrier waveform, unipolar sine carrier waveform and staircase carrier waveforms are proposed for seven-level and nine-level cascaded inverter. In each carrier waveform different techniques such as phase disposition (PD), inverted phase disposition (IPD), phase opposition disposition (POD) and alternative phase opposition disposition (APOD) are implemented. The fundamental output voltage and harmonics obtained in each method are compared with the output waveform obtained with the triangular carrier waveform. The proposed switching technique enhances the fundamental component of the output voltage and improves total harmonic distortion. The different PWM methodologies adopting the constant switching frequency multicarrier with different modulation indexes are simulated for a 1 kW, 3φ inverter using MATLAB/SIMULINK and the results are verified. The effect of switching frequency on the fundamental output voltage and harmonics are also analyzed.

Phase Current Reconstruction Techniques for Two-Phase Inverters using a Single Current Sensor

This paper proposes phase current reconstruction techniques for two-phase two-leg and two-phase four-leg inverters using a single current sensor. In the proposed methods, one phase current is sampled simultaneously with a particular branch current by using only one current sensor, and then current reconstruction algorithms are applied to extract the information on two phase currents from the sensor output. The sampled current information is periodically updated at the peak and the valley of the triangular carrier waveform in each switching cycle of pulse-width modulation (PWM). The voltage vector spaces where the phase currents can be reconstructed are evaluated. Compared to the existing method using two individual current sensors in two phases, the proposed schemes can save implementation cost since it is possible to remove one current sensor. In addition, the proposed methods are free from gain discrepancy issues between two current sensors. Simulations and experiments show excellent current reconstruction performance of the proposed methods.

Ramp based constant frequency current control for DSTATCOM

The conventional hysteresis current controller is simple to implement, has inherent peak current-limiting capability, fast dynamic response etc. However, it suffers from the demerit of variable switching frequency, which may be prohibitively high, increasing the stress levels on the switches. Although a ramp controller may be used to achieve a constant switching frequency, the selection of frequency of the triangular carrier waveform plays a crucial role in maintaining the frequency of operation same as that of the carrier. If an appropriate frequency of the carrier is not chosen, the actual current may encounter undesirable effects of over-crossing and under-crossing. This paper proposes an analytical method for proper selection of the carrier so that the above-said effects are eliminated. The method is also extended to a ramp controller with hysteresis to achieve a reduced value of the constant switching frequency. Detailed simulation has been carried out through MATLAB and an experimental prototype is also built to validate the proposed method.

Selection of carrier waveforms for PWM inverter

In this paper the influence of different carrier waveforms upon the output characteristics of PWM inverter is described in detail. When a triangular carrier waveform is used in hard-switching PWM inverters, harmonics exist in the neighborhood of the output frequency of the inverter output voltage and current due to the dead time. The triangular carrier waveform used in soft-switching PWM inverter will cause difficulties in controlling resonance-trigger time, higher loss in the resonant circuit, and less utilization of the DC bus voltage. If a sawtooth carrier is used in hard-switching PWM inverter, there will be severe distortion in the current waveform. When sawtooth carriers with alternate positive and negative slopes are used in soft-switching PWM inverters, the resonance-trigger time is easy to control, and distortion in the output voltage and current caused by the dead time will not appear.